In digital terrestrial television broadcasting and wireless local area network (WLAN), a method called orthogonal frequency division multiplex (OFDM) is used in order to avoid the effect of waveform distortion due to multipath transmission. In the OFDM, the transmission band is divided into a plurality of narrow band signals and parallel transmission is performed using each of the divided narrow band signals, thereby making it possible to perform broadband transmission while avoiding the effect of waveform distortion due to multipath transmission.
In the OFDM, multiple phase shift keying (PSK) and/or multiple quadrature amplitude modulation (QAM) are used as a modulation method for each narrow band signal. In this case, the amplitude and phase of each narrow band signal vary according to a multipath propagation path, and thus it is preferable to estimate a frequency response or an impulse response of a propagation path in order to perform demodulation of PSK and/or QAM.
In order to estimate a propagation path, a known signal is inserted as a pilot signal in part of OFDM transmission signals. A receiver extracts the pilot signal and determines the amplitude and phase variation of the pilot signal. The receiver may estimate frequency response characteristics by performing interpolation processing on the determined amplitude and phase variation of the pilot signal.
For conventional estimation of frequency response characteristics, an interpolation method, which uses a linear filter, is utilized. However, this method has a problem in that estimation accuracy significantly reduces due to noise.
Also, frequency hopping spread spectrum is known as another method for performing broadband communication in a multipath propagation path. By this method, a transmitter multiplies each narrow band modulation signal by a pseudo spreading code sequence having a wide band, thereby spreading the frequency spectrum to perform transmission. The receiver determines a cross correlation between the pseudo spreading code sequence used for the spreading and a received signal, thereby determining the original narrow band modulation signal. Also, when a cross correlation is determined, an impulse response of the multipass propagation path may be estimated from the relationship between a delay time given to the pseudo spreading code sequence and the cross correlation. However, because the impulse response characteristics determined from the cross correlation is affected by thermal noise, a problem arises in that impulse response estimation accuracy reduces.
The multipath propagation path includes finite number of paths. In such a situation, an impulse response has an impulse at a delay time position of each path and is 0 at almost other delay time positions. A technique called compressed sensing has been recently proposed, by which an object is estimated with high accuracy in the case where the object to be estimated has 0 at most positions (for example, time positions) and has a non-zero value only at partial positions, that is, the object has sparse property. A sparse vector indicates a vector consisting of elements that are almost 0.
The following are patent reference documents: Japanese Laid-open Patent Publication No. 2013-46131, Japanese Laid-open Patent Publication No. 2011-146813, Japanese Laid-open Patent Publication No. 2011-146814, Japanese National Publication of International Patent Application No. 2006-523390, Japanese Laid-open Patent Publication No. 2002-315004, and Japanese Laid-open Patent Publication No. 2000-4166.
The following are non-patent reference documents: D. L Donoho, “Compressed sensing”, IEEE Trans. on Information Theory, vol. 52, no. 4, pp. 1289-1306, April 2006 (Non-patent Reference 1), W. U. Bajwa, J. Haupt, A. M. Sayeed, and R. Nowak, “Compressed channel sensing: A new approach to estimating sparse multipath channels”, Proceedings of the IEEE, vol. 98, no. 6, pp. 1058-1076, June 2010 (Non-patent Reference 2), and J. A. Tropp, and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit”, IEEE Transactions on Information Theory, vol. 53, no. 12, pp. 4655-4666, December 2007 (Non-patent Reference 3).